What are the divisors of 2173?

1, 41, 53, 2173

There is a total of 4 positive divisors.
The sum of these divisors is 2268.
The arithmetic mean is 567.

4 odd divisors

1, 41, 53, 2173

How to compute the divisors of 2173?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2173 by each of the numbers from 1 to 2173 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2173 / 1 = 2173 (the remainder is 0, so 1 is a divisor of 2173)
2173 / 2 = 1086.5 (the remainder is 1, so 2 is not a divisor of 2173)
2173 / 3 = 724.33333333333 (the remainder is 1, so 3 is not a divisor of 2173)
...
2173 / 2172 = 1.0004604051565 (the remainder is 1, so 2172 is not a divisor of 2173)
2173 / 2173 = 1 (the remainder is 0, so 2173 is a divisor of 2173)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2173 (i.e. 46.615448083227). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2173 / 1 = 2173 (the remainder is 0, so 1 and 2173 are divisors of 2173)
2173 / 2 = 1086.5 (the remainder is 1, so 2 is not a divisor of 2173)
2173 / 3 = 724.33333333333 (the remainder is 1, so 3 is not a divisor of 2173)
...
2173 / 45 = 48.288888888889 (the remainder is 13, so 45 is not a divisor of 2173)
2173 / 46 = 47.239130434783 (the remainder is 11, so 46 is not a divisor of 2173)